Vigenere Cipher Consider the Plaintext Below. This Is the First
Vigenere Cipher
Consider the plaintext below. This is the first page of the book “And Then There Were None,” by Agatha Christie.
In the corner of a first class smoking carriage, Mr. Justice Wargrave, lately retired from the bench, puffed at a cigar and ran an interested eye through the political news in the Times. He laid the paper down and glanced out of the window. They were running now through Somerset. He glanced at his watch - another two hours to go. He went over in his mind all that had appeared in the papers about Soldier Island. There had been its original purchase by an American millionaire who was crazy about yachting and an account of the luxurious modern house he had built on this little island off the Devon coast. The unfortunate fact that the new third wife of the American millionaire was a bad sailor had led to the subsequent putting up of the house and island for sale. Various glowing advertisements of it had appeared in the papers.
Let y represent this text. In the table on the next page, the values of 100 · I(y, y(+n)) are given for 5 ≤ n ≤ 64. I’m giving the values of 100 · I(y, y(+n)) instead of the values of I(y, y(+n)) so that it’s easier to compare their values. Note that there doesn’t seem to be any way to predict which values of n have the highest index of coincidence.
1 n 100 · I(y, y(+n)) n 100 · I(y, y(+n)) n 100 · I(y, y(+n)) 5 7.207207207 25 7.264296754 45 6.389776358
6 8.120300752 26 7.264296754 46 4.960000000
7 7.981927711 27 7.298136646 47 6.410256410
8 5.882352941 28 6.531881804 48 7.223113965
9 7.854984894 29 5.607476636 49 5.144694534
10 6.051437216 30 5.928237129 50 8.212560386
11 4.848484848 31 4.062500000 51 5.161290323
12 7.435508346 32 7.355242567 52 6.462035541
13 6.534954407 33 5.485893417 53 7.443365696
14 8.675799087 34 7.849293564 54 5.672609400
15 5.640243902 35 6.918238994 55 7.792207792
16 5.038167939 36 6.456692913 56 7.479674797
17 5.810397554 37 6.309148265 57 5.211726384
18 6.891271057 38 7.898894155 58 7.830342577
19 5.368098160 39 6.012658228 59 6.535947712
20 5.990783410 40 5.546751189 60 6.219312602
21 6.769230769 41 6.190476190 61 6.557377049
22 6.163328197 42 6.995230525 62 6.075533662
23 6.790123457 43 6.528662420 63 5.427631579
24 7.264296754 44 9.569377990 64 6.425041186
2 Now, if we encrypt the plaintext by using a Vigenere cipher with keyword ”patient,” we get the ciphertext below.
XNMPI PHGNX ZSSTU IKAXP EPSLA QBDXN ZKEEK XAZMQ ECJSM QGRPP RZZEI XAAMM PLKTT BZIQY GOFBL RUTNV PTHYU EWIXN VXGTZ EAWGA GIRVG IEKMW GXSER MXUKD UZPXU XEOEQ XVVPL GMAFB CTAMX VFTSA MPNBS TAMTN ITRWW AATCD ZTEAV TDHCX BYIHX EMAWD WMPIL PTRXZ YAGXN ZVSJM WRHCK ULDMX ZWRMW EZTEA VTDTB LVLLA MKLNG DTAMV GPDHH CVFMD GHPIJ XCTHD IEBCH BAQVG SAETX UTIHT LECIT AKMHV GIHXX ECXGS TJSHM HOELM RKXSE IRQMW EKMLN WQEXV MGLDR BOMAT APNZG UTHEU GEATB EKQGN GBIET MBGPI KMAUH LALKV NSNAU WYGRP CABMA ZPNWI RNVRO NVXBY IHXTY KNGIH CWZHS EKVLB NHEAM LNWQU BTXBG IHBAP VMILX QWYTC DHNJG ATDXD SAVDA LBXUX JNYWV GNCAM MJNVI TAIXG ATNXE XUBGD PQJRH UTAME ZXGIV IRZBA LBWRN BGEPI WNUPD LIMYH GHTLP RWIOM PIFNQ SXYYR GIPNB XVGVU IWJGA THHCW RTCDB APNGS FHZWN ETVTZ MBNHG EWAVG VAWDI EMXSX UIAMH OYQXU TSAIX INKTD BVXUX EAIMV F
Let z represent this ciphertext. In the table on the next page, the values of 100·I(z, z(+n)) are given for 5 ≤ n ≤ 64. Note that now, it’s a lot easier to see which values of n have the highest index of coincidence.
3 n 100 · I(z, z(+n)) n 100 · I(z, z(+n)) n 100 · I(z, z(+n)) 5 2.702702703 25 3.869969040 45 3.194888179
6 4.962406015 26 3.255813953 46 3.520000000
7 7.981927711 27 4.658385093 47 2.724358974
8 4.826546003 28 6.531881804 48 4.975922953
9 3.172205438 29 5.140186916 49 5.144694534
10 3.177004539 30 2.808112324 50 4.025764895
11 5.454545455 31 4.218750000 51 2.419354839
12 4.248861912 32 3.442879499 52 4.846526656
13 4.103343465 33 4.075235110 53 4.530744337
14 8.675799087 34 4.081632653 54 3.889789303
15 4.725609756 35 6.918238994 55 5.357142857
16 3.206106870 36 3.779527559 56 7.479674797
17 3.822629969 37 4.574132492 57 4.723127036
18 3.675344564 38 3.475513428 58 2.610114192
19 5.061349693 39 5.063291139 59 3.594771242
20 5.069124424 40 3.645007924 60 5.237315876
21 6.769230769 41 5.079365079 61 3.606557377
22 3.697996918 42 6.995230525 62 3.940886700
23 4.475308642 43 5.095541401 63 5.427631579
24 3.863987635 44 2.711323764 64 3.624382208
4 Now, suppose that we just have the following Vigenere encrypted ciphertext.
VVHQW VVRHM USGJG THKIH TSSEJ CHLSF CBGVW CRLRY QTFSV GAHWK
CUHWA UGLQH NSLRL JSHBL TSPIS PRDXL JSVEE GHLQW KASSK UWEPW
QTWVS PGOEL KCQYF NSVWL JSNIQ KGNRG YBWLW GOVIO KHKAZ KQKXZ
GYHCE CMEIU JOQKW FWVEF QHKIJ RCLRL KBIEN QFRJL JSDHG RHLSF
QTWLA UQRHW DMWLG USGIK KFLRY VCWVS PGPML KASSJ VOQXE GGVEY
GGZML JCXXL JSVPA IVWIK VRDRY GFRJL JSLVE GGVEY GGEIA PUUIS
FPBTG NWWMU CZRVT WGLRW UGUMN CZVIL E
Let x represent this ciphertext. In the table on the next page, the values of 100·I(x, x(+n)) are given for 1 ≤ n ≤ 30.
5 n 100 · I(x, x(+n)) n 100 · I(x, x(+n)) 1 4.242424242 16 3.492063492
2 4.255319149 17 4.140127389
3 4.878048780 18 4.472843450
4 4.281345566 19 3.525641026
5 7.361963190 20 6.430868167
6 3.692307692 21 5.483870968
7 4.012345679 22 4.530744337
8 4.024767802 23 4.870129870
9 2.173913043 24 5.211726384
10 4.361370717 25 6.862745098
11 4.062500000 26 3.278688525
12 5.956112853 27 1.973684211
13 4.088050314 28 3.300330033
14 4.731861199 29 3.973509934
15 8.227848101 30 8.305647841
6 Now look at the first letter of each iteration of the key. That is, look at x0, x5, x10, x15, x20,.... These letters are all shifted by the same amount. The letters we have are
VVUTTCCCQG CUNJTPJGKU QPKNJKYGKK GCJFQRKQJR QUDUKVPKVG GJJIVGJGGP FNCWUCE.
A partial frequency count for this message is below. All other letters appear fewer than 5 times. CGJKQUV 7 9 8 8 5 6 5
Now look at the second letter of each iteration of the key. That is, look at x1, x6, x11, x16, x21,.... These letters are all shifted by the same amount. The letter ‘G’ appears 10 times and ‘S’ occurs 12 times, and no other letter appears nearly as much.
Now look at the third letter of each iteration. A partial frequency count is below. All other letters appear fewer than 3 times.
DEGHKLQRSVW 3 3 3 5 4 10 3 5 3 8 7
7 If we guess that the keyword used for this Vigenere cipher was ‘codes’ and decipher the message, we get the following plaintext.
The method used for the preparation and reading of code messages is simple in the extreme and at the same time impossible of translation unless the key is known. The ease with which the key may be changed is another point in favor of the adoption of this code by those desiring to transmit important messages without the slightest danger of their messages being read by political or business rivals, etc.
Since this decrypts to something that makes sense in English, we can be confident that we have decoded it correctly. For a message of this length, it would be extremely unlikely for two different keys to yield a plaintext that makes sense.
This is in fact the correct plaintext. It is from an article in Scientific American, Supple- ment in 1917. Note that our work in this class proves that the opinion it gives is wrong!
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